establish identity
sec 0/1 + sec0 = 1 - cos0/sin^2 0
Do you mean sec 0/(1 + sec 0) ?
On the right side,do you mean
(1 - cos 0)/sin^2 0?
You need to use parentheses to make your equations unambiguous.
To establish the identity sec(0/1) + sec(0) = (1 - cos(0)) / sin^2(0), we will simplify the left-hand side of the equation and then simplify the right-hand side of the equation.
Starting with the left-hand side:
sec(0/1) + sec(0)
The secant function is the reciprocal of the cosine function, so sec(θ) = 1 / cos(θ).
Therefore, we can rewrite the left-hand side as:
1 / cos(0/1) + 1 / cos(0)
Now, cos(0/1) is equivalent to cos(0), which is equal to 1. Similarly, cos(0) is also equal to 1.
Substituting these values, we get:
1 / cos(0) + 1 / cos(0)
Since both terms are equal, we can combine them:
2 / cos(0)
Using the identity cos(θ) = 1/sec(θ), we can simplify further:
2 / cos(0) = 2 / ( 1 / sec(0) ) = 2 × sec(0)
Therefore, the left-hand side simplifies to:
2 × sec(0)
Now, let's simplify the right-hand side of the equation:
(1 - cos(0)) / sin^2(0)
Since cos(0) is equal to 1, we have:
(1 - 1) / sin^2(0)
Simplifying further:
0 / sin^2(0) = 0
Now, let's compare the simplified left-hand side and right-hand side:
2 × sec(0) = 0
From here, we can see that the two sides are not equal. Therefore, the given equation sec(0/1) + sec(0) = (1 - cos(0)) / sin^2(0) is not an identity.